Solve the given inequality and show the graph of the solution on number line: $ 3(1-x) <2 (x +4)$

1 Answer

Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality.

Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality.

If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e $ '>'$ sign changes to $'<' $ and $'<'$ changes $'>'$ .

To represent solution of linear inequality involving one variable on a number line, if the inequality involves $\geq $ or $\leq$ are draw filled circle (0) on the number is included in the solution set.

If the inequality involves $'>'$ or $'<'$ we draw open circle (0) on the number line to indicate the number is excluded from the solution set.

Step 1:

The given inequality is $ 3(1-x) < 2( x+4)$

=> $ 3-3x < 2x+8$

Adding -8 and 3x on both sides of the inequality.

$=> 3-8 < 2x +3x$

$=> -5 < 5x$

Dividing both sides of the inequality by a positive number 5.

$=> \large\frac{-5}{5} < \frac{5x}{5}$

$=> -1 < x$

Step 2:

All numbers greater than -1 represent the solution of the given inequality .